There are many reasons why you might want to change your name, whether it's because of change in marital status or you don't like your birth name. While in US, the laws vary from state to state, though the process is similar.
Generally, a petition will be filed with the court citing your reason for wanting a name change to initiate the process. Depending on the court you file in, there might be a hearing that you may be required to attend and publication of the name change notice might be required in a newspaper of general circulation in the county in which you reside. If your petition is approved, you will receive an order of name change from the court.